Dannika solved this equation: -2(x + 4) = 10. Below are her steps. Step 1: −2 (x+4)=10 Step 2: −2(x) + −2(4) =10 Step 3: −2x +−8 =10 Step 4: −8 −8 Step 5: −2x =2 Step 6: ÷−2 ÷−2 Step 7: x=1 Analyze Dannika's work. Dannika made 2 mistakes.

The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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Answer:

y=40°

Z + Y = 70°

z. = 70°-40°

z. = 30°

POH=X

=180-70

=110°

Answer:

-4

Step-by-step explanation:

6(a+(-1)) = 8a + 2

then:

6(a-1) = 8a + 2

6*a + 6*-1 = 8a + 2

6a - 6 = 8a + 2

6a - 8a = 2 + 6

-2a = 8

a = 8/-2

a = -4

Check:

6(-4-1) = 8*-4  +  2

6*-5 = -32 + 2 = -30

Answer:

D: A

Step-by-step explanation:

It is not CD as it doesn't cover the whole line, D is just a proportion of the line and AC is only less than half.

Answer:

I believe the answer is 240.

Step-by-step explanation:

Answer:

240 calories each day

Step-by-step explanation:

According to the information Lacey read, a cat weighing p pounds needs to eat a total of 30p calories each day to stay healthy. Since Lacey's cat, Muffin, weighs 8 pounds, she needs to eat 30 * 8 = <<30*8=240>>240 calories each day to stay healthy. Therefore, Lacey should feed her cat a total of 240 calories each day in order to ensure that it receives the proper nutrition and stays healthy.

The total cost of materials and labor for the office space, considering a tile unit cost of P300 and labor cost equal to the materials cost, amounts to P63,000.

To calculate the total cost of materials and labor, we first need to determine the cost of the tiles. Given that the unit cost of a certain tile is P300, we can multiply this by the area of the office space to find the total cost of the tiles. The office space has an area of 63 sqm, so the total cost of the tiles is P300 * 63 = P18,900.

Next, we need to calculate the labor cost, which is 100% of the materials cost. Since the materials cost is P18,900, the labor cost will be equal to P18,900. Therefore, the total cost of labor is also P18,900.

To find the total cost of materials and labor, we add the cost of the tiles (P18,900) and the labor cost (P18,900): P18,900 + P18,900 = P37,800.

Therefore, the total cost of materials and labor for the office space is P37,800.

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The underlying function f(x - i) that generates the observed points f'(x - i) in the plot can be determined by integrating the observed points. By integrating f'(x - i), we can obtain f(x - i) up to a constant of integration.

The constant of integration can be determined by incorporating additional information or constraints related to the problem or by considering the behavior of the function at a specific point.

To find the underlying function f(x - i) that generates the observed points f'(x - i), we need to integrate the observed points.

Integration is the reverse process of differentiation, so by integrating f'(x - i), we can recover f(x - i) up to a constant of integration.

The constant of integration arises because integration does not provide a unique solution.

The constant represents an arbitrary additive term that can vary depending on the specific problem or additional constraints.

To determine the constant of integration, we may need additional information or consider specific conditions related to the problem.

It is also important to note that the accuracy of estimating the underlying function f(x - i) depends on the quality and quantity of the observed data points f'(x - i). More data points and precise measurements can lead to a better estimation of the underlying function.

Additionally, the behavior of the function at a specific point can provide valuable insights for determining the constant of integration and refining the estimation of the underlying function.

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Answer: A!!

Step-by-step explanation:

i just got it right lol

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the engineer's claim. Hence, the engineer's claim is false.

To answer this question, we need to conduct a hypothesis test with a significance level of α = 0.05. The null hypothesis (H0) is that the true mean commute time is equal to or greater than 25 minutes, while the alternative hypothesis (Ha) is that the true mean commute time is less than 25 minutes. We can use a one-sample t-test to test this hypothesis, where the test statistic is calculated as:
t = (sample mean - hypothesized mean) / (standard deviation/sqrt (sample size))
t = (24.6 - 25) / (13 / sqrt(1923))
t = -1.53

Using a t-distribution table with degrees of freedom (df) equal to the sample size minus 1 (df = 1922), we find that the p-value for this test is 0.064. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the engineer's claim that the mean commute time is less than 25 minutes. The deviation from the hypothesized mean is -0.4 which is less than 1 standard deviation, hence we cannot say with confidence that the mean commute time is less than 25 minutes.

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Bianca runs approximately 146.4 yards across the diagonal of the soccer field.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.

Given, the soccer field at Bianca’s school has a length of 120 yards and a width of 85 yards.

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal = √(120² + 85²)

diagonal ≈ 146.4 yards

Therefore, Bianca runs approximately 146.4 yards across the diagonal of the soccer field.

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Answer:

every other student who enters the school

Step-by-step explanation:

It is given that the middle school students have an average height of 5.25 feet. The students belongs to Seton Grove School.

It means that every student who comes to this school or enters the school has a height that is around 5 feet or more.

Thus we can say that every other student who enters the school has a average height of 5.25 feet.

This sample makes the generalization about the heights of the school students valid.

Answer:

c

Step-by-step explanation:

correct on edmentum / plato

Answer:

its 3

Step-by-step explanation:

The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.

To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.

When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.

Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).

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Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ - 1/3 (y - x)

Now, We can expand the expression as;

⇒ - 1/3 (y - x)

⇒ - 1/3 × y - 1/3 × - x

⇒ - 1/3y + 1/3x

Thus, Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

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The factored form of the quadratic equation 2x² + 25x + 50 is (2x + 5)(x + 10)

Factoring quadratics is a method of expressing the quadratic equation ax² + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax² + bx + c = 0.

Therefore, let's factor the equation 2x² + 25x + 50.

2x² + 25x + 50

The two numbers one can multiply and add to get 100 and 25 respectively are 20 and 5.

Therefore,

2x² + 20x + 5x + 50

2x(x + 10)+ 5(x + 10)

Therefore,

(2x + 5)(x + 10)

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Answer:

68°

Step-by-step explanation:

since the ball is placed or comes from a straight line (which is the wall) it means that when you add all those angles the final answer has to be 180 because angles in a straight line add up to 180°

68°+44°+1=180

112°+1=180

1=180-112

=68°

I hope this helps

The measure of ∠1 is 68 degrees.

We have Lisa who kicked a ball against the wall at the indicated angle.

We have to determine the measure of the angle 1 in degrees.

A straight line has an angle of 180 degrees.

According to question, we have -

∠3 = 68 degrees

∠2 = 44 degrees

Therefore -

∠3 + ∠2 + ∠1 = 180

68 + 44 + ∠1 = 180

112 + ∠1 = 180

∠1 = 180 - 112

∠1 = 68 degrees

Hence, the measure of ∠1 is 68 degrees.

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The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.

Given data;

A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.

We need to get the probability that the mpg for a randomly selected compact car would be more than 30.

Therefore;

Mean = μ = 31

Standard deviation = σ = 1.2

Let;

P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)

               = P(Z > -0.833)

               = 0.797

Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.

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Answer:

AAS

Step-by-step explanation:

have a good day:) .....

Answer:

No, Anthony is not correct.

Step-by-step explanation:

K is at (-4, 8), L is at (-7, 4), M is at (-2, 1)

KL

\( \sqrt{ {( - 4 - ( - 7))}^{2} + {(8 - 4)}^{2} } \)

\( \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5\)

LM

\( \sqrt{ {( - 7 - ( - 2))}^{2} + {(4 - 1)}^{2} } \)

\( \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} \)

KM

\( \sqrt{ {( - 4 - ( - 2))}^{2} + {(8 - 1)}^{2} } \)

\( \sqrt{ {( - 2)}^{2} + {7}^{2} } = \sqrt{4 + 49} = \sqrt{53} \)

From these, it follows that KLM is not an isoceles triangle.

Answer:

S = $10.20

Step-by-step explanation:

s = 12 - .15 (12)

s = 12 - 1.80

s = $10.20

If 15% comes off the price, then 85% of the price is left to pay. (100 - 15 = 85)

12 x .85 = $10.20

Answer:

100, 101, 102, 103, 104

Step-by-step explanation:

Basically, if the units (or ones, it's the same thing) digit of the first number is 0, the units digit of the second number should be 1, then 2, and so on. Therefore, one possible list of numbers is as follows: 100, 101, 102, 103, 104.

Answer:

1. is 29.3in^3

2. 268.08

4/3pi(r)^3

4/3pi(4)^3

= 268.08

Rounded to the nearest tenth is 268.1

Answer:

10.63

Step-by-step explanation:

Use pythagorean theorem:

c=√(a^2+b^2)

√(7^2+8^2)

√(49+64)

√(113)

10.63

The constraint can then be written as: S ≤ 0.07 × T. This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.

The constraint can then be written as: S ≤ 0.07 × T, This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.

We are given that the amount of sulfur relative to the total output produced of chemical X may not exceed 7%. To express this constraint in a linear programming model, we can use the following equation:

Sulfur Content ≤ 0.07 × Total Output

Here, the "Sulfur Content" represents the total amount of sulfur present in the chemical blend, while "Total Output" refers to the total amount of chemical X produced. By setting the constraint to be less than or equal to 7% (0.07) of the total output, we are ensuring that the sulfur content does not exceed the given limit.

In a linear programming model, we usually use variables to represent quantities. Let S represent the Sulfur Content and T represent the Total Output. The constraint can then be written as:

S ≤ 0.07 × T

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The SAT has two sections, Mathematics and Reading, and the combined score is reported on a scale of 400 to 1600. The Z-score is (1600 - 1003) / 220 = 2.37.

The normal distribution is widely used in statistics and is a useful tool for analyzing many types of observations and data in nature and the sciences. Standard deviation is a measure of the spread of the distribution and can be used in computation of various probabilities.

To determine the proportion of SAT scores that were reported as 1600 or higher, we need to find the number of standard deviations above the mean a score of 1600 would be.

Using the normal distribution and Z-scores, we can calculate the Z-score for a score of 1600, given the mean of 1003 and standard deviation of 220.

The Z-score is (1600 - 1003) / 220 = 2.37.

This means that a score of 1600 is 2.37 standard deviations above the mean.

To find the proportion of scores that are higher than 1600, we can use a standard normal table to look up the area under the normal curve to the right of the Z-score of 2.37.

This proportion is approximately 0.9906,

meaning that approximately 99.06% of the SAT scores were lower than 1600, and only 0.94% of the scores were higher and reported as 1600.

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